Reply to Adams: Multi-Dimensional Edge Interference
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Citation
Eagle, Nathan et al. “Reply to adams: Multi-dimensional edge
inference.” Proceedings of the National Academy of Sciences
107.9 (2010): E31. Copyright ©2010 by the National Academy of
Sciences
As Published
http://dx.doi.org/10.1073/pnas.0913678107
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National Academy of Sciences (U.S.)
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Final published version
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Thu May 26 18:26:28 EDT 2016
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http://hdl.handle.net/1721.1/61402
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LETTER
Reply to adams: Multi-dimensional
edge inference
We completely agree with adams that, in social network analysis, the particular research question should drive the definition
of what constitutes a tie (1). However, we believe that even
studies of inherently social phenomena, such as the spread of
influence (2) or supposed “social contagions” (3), can benefit
strongly from a focus on objective behavioral data (4).
For instance, the conventional wisdom is that social influence
only travels along self-perceived ties. However, in truth, it remains unknown how much is being hidden from us by
recency and saliency cognitive filters (5), and significant social
influence may, in fact, travel across unperceived ties. Behavioral data are not prone to such filters and thus, when used
properly, may shed considerable light on such
important questions.
We also agree that an appropriate combination of selfreported edges and behavioral data, as suggested by adams,
has the potential to address previously unanswered questions
about the underlying dynamics of a group of interacting individuals. However, we urge caution in combining these very
different kinds of data: a network with multiple types of edges,
such as self-reported ones with those inferred by a factor analysis
of behavioral data, can obscure important nuances that should
be leveraged through parallel analyses rather than flattened into
a single monolithic network. Indeed, there are times when it may
be more appropriate to use “raw” behavioral data instead of the
nonparametric output of a factor analysis. For instance, Fig. 1
shows how the self-reported friendship network compares with
networks corresponding to communication, proximity on Saturday night, and travel, showing some marked differences. Understanding how behavioral data may influence, conflict with, or
derive from the construction of the self-reported network is an
interesting future line of inquiry.
It should, however, be possible to develop significantly better
edge inference techniques by combining information at the local
level of the dyad (including edge and node attributes) with
information about ties elsewhere in the network. For instance, it
was recently shown that the nested or hierarchical structure of
entire social networks can predict missing dyadic links with high
accuracy (6). Mathematically, this general approach has
the form:
P xyfriendship jxybehavior ; ΔTE=xy
where Pðxyfriendship Þ is the probability of a friendship between x
and y, xybehavior is the local behavioral variables associated with
the dyad, and ΔTE=xy represents how the global topological summary statistics associated with the network would change with
the addition/removal of the edge between x and y.
To conclude, we point out that purely behavioral data, of
course, are not a panacea, and their proper interpretation can
www.pnas.org/cgi/doi/10.1073/pnas.0913678107
Fig. 1. Networks representing reported friendship, phone communication,
proximity on Saturday night, and travel (a dyad is connected if proximate
while being associated with more than 30 unique cellular towers). Nodes
reflect the two groups of colleagues—the first year business school students
and the Media Laboratory students working together in the same building
on campus.
be difficult without appropriate cognitive models. Instead,
the use of behavioral data in social network analysis provides
a highly complementary and very powerful tool for understanding social phenomena of all kinds (4). It also provides
an objective way to identify, wrestle with, and mitigate the
cognitive biases humans express, which often muddy the
waters for scientific understanding of human phenomena.
We strongly believe that the appropriate collection and
analysis of such behavioral data have crucial roles to play in
social network analysis.
Nathan Eaglea,b,1, Aaron Clauseta, Alex (Sandy) Pentlandb, and
David Lazerc,d
a
Santa Fe Institute, Santa Fe, NM 87501; bMassachusetts Institute of
Technology Media Laboratory, Cambridge, MA 02139; cNortheastern University, Boston, MA 02115; and dHarvard University,
Cambridge, MA 02138
1. adams j (2010) Distant friends, close strangers? Inferring friendships from behavior.
Proc Natl Acad Sci USA 107:E29–E30.
2. Watts DJ, Dodds PS (2007) Influentuals, networks, and public opinion formation. J
Consum Res 34:441–458.
3. Cohen-Cole E, Fletcher JM (2008) Detecting implausible social network effects in acne,
height, and headaches: longitudinal analysis. BMJ 337:a2533.
4. Eagle N, Pentland AS, Lazer D (2009) Inferring friendship network structure by using
mobile phone data. Proc Natl Acad Sci USA 106:15274–15278.
5. Freeman L, Romney A, Freeman S (1987) Cognitive structure and informant accuracy.
Am Anthropol 89:310–325.
6. Clauset A, Moore C, Newman MEJ (2008) Hierarchical structure and the prediction of
missing links in networks. Nature 453:98–101.
Author contributions: N.E., A.S.P., and D.L. designed research; N.E. performed research;
N.E. analyzed data; and N.E. and A.C. wrote the paper.
The authors declare no conflict of interest.
1
To whom correspondence should be addressed. E-mail: nathan@mit.edu.
PNAS | March 2, 2010 | vol. 107 | no. 9 | E31